@Article{NMTMA-2-326,
author = {R. Shi, T. Wei and H. H. Qin},
title = {A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2009},
volume = {2},
number = {3},
pages = {326--340},
abstract = {<p style="text-align: justify;">This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain $0 &lt;x\le 1$, $y\in R$. The Cauchy data at $x=0$ is given and the solution is then sought for the interval $0&lt; x\le 1$. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2009.m88032},
url = {http://global-sci.org/intro/article_detail/nmtma/6027.html}
}